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Chapter 9: Q.23 (page 548)

You read that a statistical test at significance levelα=0.05 has power 0.78. What are the probabilities of Type I and Type II errors for this test?

Short Answer

Expert verified

The probabilities are Type I = 0.05and Type II error = 0.22

Step by step solution

01

Introduction

Error emerges with regards to independent direction, where the likelihood of error might be considered similar to the likelihood of pursuing an off-base choice and which would have an alternate incentive for each kind of error.

02

Explanation

We know significance level α=0.05 and power is 0.78

Probability of type I error = α=0.05

Probability of type I error localid="1654151980897" 2-power = 1-0.78=0.22

Hence the probabilities are Type I = 0.05and Type II error = 0.22

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Most popular questions from this chapter

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using A=0.01 instead of A=0.05.

(c) using A=0.05 instead of A=0.01.

(d) giving the drug to 25 randomly selected students instead of 50.

(e) using a two-sided test instead of a one-sided test.

In planning a study of the birth weights of babies whose mothers did not see a

doctor before delivery, a researcher states the hypotheses as

H0:μ<1000gramsHa:μ=900grams

You are testing HO:μ=10Hα:μ<10against based on an SRS of 20observations from a Normal population. The tstatistic is . t=-2.25The P-value

(a) falls between 0.01and0.02

(b) falls between0.02and0.04

(c) falls between0.04and0.05

(d) falls between .05and0.25.

(c) is greater than0.25.

Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, a reader posed this question: "Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I'll get at least one apple?" Suppose that the wheels spin independently and that the fre symbols are equally likely to appear on each wheel in a given spin.

(a) Find the probability that the slot player gets at least one apple in one pull of the lever. Show your method clearly.

(b) Now answer the reader's question. Show your method clearly.

After checking that conditions are met, you perform a significance test of H0:μ=1versus Hα:μ≠1. You obtain a Pvalue of 0.022. Which of the following is true?

(a) A95%confidence interval for μwill include the value 1

(b) A 95%confidence interval forμwill include the value 0.

(c) A99% confidence interval forμwill include the value 1

(d) A 99%confidence interval for μwill include the value 0

(e) None of these is necessarily true.
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